1. ABCD is an isosceles trapezoid. m < A = 6x + 12 and m < d = 2x + 20. Angles B&C are congruent. What is the measure of angles B&C?

2. QRST is a rectangle. RS = 12k +5 and QT = 145. what is the value of 'k'?

∠ B = 123°, ∠ D = 57°

Step-by-step explanation:

Each lower base angle is supplementary to the upper base angle on the same side.

∠ A and ∠ D are on the same side, then

6x + 12 + 2x + 20 = 180

8x + 32 = 180 ( subtract 32 from both sides )

8x = 148 ( divide both sides by 8 )

x = 18.5

Thus

∠ A = 6x + 12 = 6(18.5) + 12 = 111 + 12 = 123°

∠ D = 2x + 20 = 2(18.5) + 20 = 37 + 20 = 57°

The lower base angles and the upper base angles are congruent, so

∠ B = ∠ A = 123°

∠ C = ∠ D = 57°

Step-by-step explanation:

#1). It could be good to provide us with the picture, because the answer depends from the angle we choose for letter A.

--- If angle A is acute, then m∠A = m∠D

and

6x + 12 = 2x + 20 ⇒ x = 2

m∠A = m∠D = 24°

m∠B = m∠C = 180° - 24° = 156°

--- If angle A is obtuse, then m∠A + m∠D = 180°

and

6x + 12 + 2x + 20 = 180 ⇒ x = 18.5

m∠A = m∠B = 6(18.5) + 12 = 123°

m∠D = m∠C = 2(18.5) + 20 = 57°

#2). 12k + 5 = 145

12k = 140

k = =

3.4 pizzas

step-by-step explanation:

given is a scatter plot showing number of pizzas sold during weeks for different issues of coupon

y represents number of pizzas sold and x number of coupons issued

y is marked verticaly and x horizontally

the trend line is given as

y =3.4x+43

this says that even when no coupon is issued pizzas sold will be 43

and rate of change of pizza sold for 1 unit of coupon = slope = 3.4

i.e. when x increases by 1 unit y increases by 3.4 units

hence for each additional coupon issued 3.4 pizzas more will be sold

sine

step-by-step explanation: